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Boundedness of Generalized Fractional Integral Operators on Orlicz Spaces Near L1 Over Metric Measure Spaces

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Abstract

We are concerned with the boundedness of generalized fractional integral operators Iϱ,τ from Orlicz spaces LΦ(X) near L1(X) to Orlicz spaces LΨ(X) over metric measure spaces equipped with lower Ahlfors Q-regular measures, where Φ is a function of the form Φ(r) = rl(r) and l is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.

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Authors and Affiliations

  1. Nagasakihokuyodai High School, Nagasaki, 851-2127, Japan

    Daiki Hashimoto

  2. Faculty of Education, Oita University, Dannoharu Oita-city, 870-1192, Japan

    Takao Ohno

  3. Department of Mathematics, Graduate School of Education, Hiroshima University, 1-1-1, Kagamiyama, Higashi-Hiroshima, 739-8524, Japan

    Tetsu Shimomura

Authors
  1. Daiki Hashimoto
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  2. Takao Ohno
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  3. Tetsu Shimomura
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Correspondence to Takao Ohno.

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Hashimoto, D., Ohno, T. & Shimomura, T. Boundedness of Generalized Fractional Integral Operators on Orlicz Spaces Near L1 Over Metric Measure Spaces. Czech Math J 69, 207–223 (2019). https://doi.org/10.21136/CMJ.2018.0258-17

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  • DOI: https://doi.org/10.21136/CMJ.2018.0258-17

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